SETTING DETERMINING EQUATIONS FOR THE FLOW NONLINEAR ELASTIC-PLASTIC MATERIAL

Abstract

The question of the choice of two scalar parameters, respectively, the two defining equations of the flow of the particular model of a nonlinear elasticity-plasticity to limit the growth of elastic anisotropy is considered. The elastic properties of the material are described by the generalized Murnaghan law of elasticity. The model is constructed with the assistance of the potentiality principle of defining equations in the stress rate, which lets determine the yield surface deviator cross-section. To simplify the case the material assumed to be perfectly elastic-plastic. The values of the first and second parameters are relative parts of dissipative specific deformation power and projections on the surface of deviator section of yield surface of criterion deviator operator. They are part of the differential equations for determining a specific potential energy of elastic deformation and the Cauchy stress tensor. In the case when the first parameter is independent on the strain rate tensor, the system of equations generates the minimum value of the parameter. This choice makes too large errors in the condition of biaxial state of stress in numerical modeling of Bridgman’s experiments under biaxial compression. The value of the second parameter has to be substantially smaller. The first parameter is chosen while carrying out of this requirement when the first parameter depends on the angle between the normal vector to the surface deviator section and “vector” of strain rate (in basic, epitaxial experiments). The choice of these parameters significantly limits the growth of elastic anisotropy, as it is shown by numerical simulation of biaxial loading. It can be updated by use of additional experimental data of these loadings.